How to fill a volume plot of a vector valued functions (with 3 variables)

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Niklas Kurz 2021-6-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/849915-how-to-fill-a-volume-plot-of-a-vector-valued-functions-with-3-variables

编辑： Niklas Kurz 2021-6-9

Again, I'm ascending new ground, now dealing with volume plots. I'm aware of Matlabs documentary concering this topic. But it doesn't seem to cover my problem. It's about plotting:

where

To the best of my knowldege this function will map a cuboid to

. So it should be representable without reducing any dimension. I feel like inconvenient doing this in Matlab, since there doesn't seem to exist some nice functions like mesh or surf for volumes, so I just can't

[u,v,w] = meshgrid(-1:0.1:1);
x = u.^2+u;
y = v.^2+v;
z = z.^2+z;
mesh(x,y,z) %... just defined for surfaces. 

Nevertheless Is there some equivalence for volumes?

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KSSV 2021-6-7

Have a look on slice

Niklas Kurz 2021-6-8

编辑：Niklas Kurz 2021-6-8

Isn't slice made for plotting scalar functions of 4th dimension? I haven't been using isosurface yet, but its plots look like 2-dimensional manifolds. For my purpose you must think about a

filled cube, that is being deformed in

by the function φ. At least that's how I think about it. Briefly speaking I search for a function like mesh that maps a plane of points in

and inderpolates the distance between the resulting mapping. Just for Volumes.

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回答（1 个）

Matt J 2021-6-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/849915-how-to-fill-a-volume-plot-of-a-vector-valued-functions-with-3-variables#answer_719070

See quiver3.

https://www.mathworks.com/help/matlab/ref/quiver3.html

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Niklas Kurz 2021-6-9

编辑：Niklas Kurz 2021-6-9

Yea, that's true: a vector field is a vector valued function, but a vector falued function is not a vector field. Here I'm just given a vector valued function, whose mapped domain I'd like to visulaize (as connected points, like mesh)

Niklas Kurz 2021-6-9

编辑：Niklas Kurz 2021-6-9

probably matlab lecks the ability of doing that, because I haven't seen fully 3D filled objects being plotted yet. Just the outline. So maybe I've to finde a parametrization